This means the total cable length is 3.75m, which is above the 3m
recommendation.
This is a misconception. The "3m recommendation" is based on use of generally-practiced consumer-grade raw cables having two USB-defined connectors. In theory the channel length is limited only by ability of the cable to propagate signals with differential loss of less than -25dB at 7.5 GHz. If you can make a 20-m cable from very expensive materials and/or finger-size thick that meets this specification, the USB 3.x link should work just fine.
However, you are planning to break the link into 4 segments, and thus introduce 4 extra connectors. Connectors are usually the worst to maintain characteristic impedance, and all board-to-connector (or cable-to-connector attachment) fan-out has horrible variability and usually introduces impedance mismatches, and heavy inter-symbol interference results. This is the primary reason why USB standard strongly discourages the use of passive cable extenders, the necessary quality of interconnect is simply not achievable in consumer-grade production. So your "passive" approach will require the use of very expensive military-grade connectors and careful design of internal PCBs or whatever do you plan to use inside your enclosures.
As you mention, the other option is to use either a re-driver (I would use two of them, at the output of each enclosure), or a low-port-count USB 3.0 hub. The use of two classic analog re-drivers in series is however questionable, since each redriver will introduce extra jitter, which might kill the link. The solution is in new class of USB devices called re-timers, but they are fairly new devices, I am not sure if they already hit the market, and have no experience with them.
In all above cases the success is highly questionable or will take a lot of efforts and expensive equipment to tune the link. I would still try to find a way to connect your PC with the cam with one-segment active extender, preferably based on fiber-optics, just like the cables offered by Corning Communication.
